The equivalent sand-grain roughness model is an empirical model initiated by Schlichting for predicting skin friction and heat transfer for turbulent flows over rough surfaces. For the equivalent sand-grain roughness model, rough surfaces with various features are compared to data from Nikuradse concerning flow in pipes with varying sizes of sieved sand glued to the wetted surface. Rough surfaces are assigned a value of equivalent sand-grain roughness height based on comparisons with Nikuradse’s fully rough data. Recent literature on the equivalent sand-grain roughness method has involved seeking correlations for equivalent sand-grain roughness height based on roughness metrics such as height, shape, and density. The Sigal-Danberg parameter has demonstrated the most promise for correlating the available equivalent roughness height data to geometric surface information. The Sigal-Danberg parameter was recently modified to include the mean surface elevation as an important parameter. While the modified Sigal-Danberg parameter provides a unified correlation for the equivalent sand-grain roughness height, the new formulation does not improve the scatter of the experimental data around the correlation. An uncertainty analysis is presented to evaluate the uncertainty of equivalent sand-grain roughness height predictions using the unified correlation. The analysis begins by estimating the uncertainties in the experimental measurements of Schlichting, and the uncertainty propagation is evaluated through each step of the equivalent sand-grain method development. The uncertainty associated with using empirical equations and conceptual uncertainties not associated with experimental measurements are also discussed. The result is an improved understanding of and uncertainty quantification for skin friction and heat transfer predictions made using equivalent sand-grain roughness methods.

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